What is 3/2 ln|(-0.5-1)|-3/2 ln|(-1-1)| ?

The solution to 3/2 ln|(-0.5-1)|-3/2 ln|(-1-1)| is ln(0.64951…)

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simplify 3/2 ln|(-0.5-1)|-3/2 ln|(-1-1)|

simplify

\frac{3}{2} ln ∣ (- 0.5 - 1) ∣ - \frac{3}{2} ln ∣ (- 1 - 1) ∣

ln (0.64951 \dots)

Decimal Notation

- 0.43152 \dots

Solution steps

\frac{3}{2} ln ∣ (- 0.5 - 1) ∣ - \frac{3}{2} ln ∣ (- 1 - 1) ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{2} ln ∣ (- 1 - 0.5) ∣ = ln (∣ (- 1 - 0.5) ∣^{\frac{3}{2}})

= ln (∣ (- 1 - 0.5) ∣^{\frac{3}{2}}) - \frac{3}{2} ln ∣ (- 1 - 1) ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{3}{2} ln ∣ (- 1 - 1) ∣ = ln (∣ (- 1 - 1) ∣^{\frac{3}{2}})

= ln (∣ (- 1 - 0.5) ∣^{\frac{3}{2}}) - ln (∣ (- 1 - 1) ∣^{\frac{3}{2}})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (∣ (- 0.5 - 1) ∣^{\frac{3}{2}}) - ln (∣ (- 1 - 1) ∣^{\frac{3}{2}}) = ln (\frac{∣ - 1 - 0.5 ∣ ^{\frac{3}{2}}}{∣ - 1 - 1 ∣ ^{\frac{3}{2}}})

= ln (\frac{∣ - 0.5 - 1 ∣ ^{\frac{3}{2}}}{∣ - 1 - 1 ∣ ^{\frac{3}{2}}})

\frac{∣ ( - 0.5 - 1 ) ∣ ^{\frac{3}{2}}}{∣ ( - 1 - 1 ) ∣ ^{\frac{3}{2}}} = 0.64951 \dots

= ln (0.64951 \dots)

ln (x^{3} \cdot (x + 2))

\frac{2 cos ( 2 ln ( x ) )}{x ^{2}} + x^{3}

2 ln (a) - \frac{1}{2} ln (b)

5.8 + lo g_{10} (\frac{0.015}{0.4})

ln ∣ x ∣ + ln ∣ sin (x) ∣

What is 3/2 ln|(-0.5-1)|-3/2 ln|(-1-1)| ?
The solution to 3/2 ln|(-0.5-1)|-3/2 ln|(-1-1)| is ln(0.64951…)